Question

Запишіть рівняння прямої, яка проходить через точки A(2;-4) і мае кутовий коефіціент k, якщо: а)k=2 б)k=1 в)k=-3 г)k=-0,5? ОЧЕНЬ НАДО!

Answer 1

Equation of a Line Passing Through Point A(2,-4) with Slope k

To find the equation of a line passing through point A(2,-4) with a slope of k, we can use the point-slope form of a linear equation:

y - y1 = m(x - x1)

where (x1, y1) represents the coordinates of the given point, and m represents the slope of the line.

Let's calculate the equations for different values of k:

a) When k = 2: Substituting the values into the point-slope form, we have: y - (-4) = 2(x - 2)

b) When k = 1: Substituting the values into the point-slope form, we have: y - (-4) = 1(x - 2)

c) When k = -3: Substituting the values into the point-slope form, we have: y - (-4) = -3(x - 2)

d) When k = -0.5: Substituting the values into the point-slope form, we have: y - (-4) = -0.5(x - 2)

Now, let's simplify each equation to determine the final form:

a) When k = 2: y + 4 = 2x - 4

b) When k = 1: y + 4 = x - 2

c) When k = -3: y + 4 = -3x + 6

d) When k = -0.5: y + 4 = -0.5x + 1

These are the equations of the lines passing through point A(2,-4) with different slope values.